Acoustic logging apparatus and method for anisotropic earth formations

ABSTRACT

The patent discloses a signal processing technique for determining the fast and slow shear wave polarizations, and their orientation, for acoustic waves in an anisotropic earth formation. The signal processing method decomposes composite received waveforms a number of times using a number of different strike angles. The decomposed signals are used to create estimated source signals. The estimated source signals are compared in some way to obtain an objective function. Locations in a plot where the objective function reaches minimum values are indicative of the acoustic velocity of the fast and slow polarizations within the formation.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is related to co-pending application Ser. No.10/025,528, filed Dec. 18, 2001 titled “Acoustic Logging Apparatus AndMethod” and is a continuation of application Ser. No. 10/025,157 filedDec. 19, 2001, titled “Acoustic Logging Apparatus and Method forAnisotropic Earth Formations.”

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

Not applicable.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention generally relates to acoustic well logging. Moreparticularly, the present invention relates to determining slow and fastshear wave velocities and orientations in an anisotropic earthformation.

2. Description of the Related Art

It is a well known phenomena that certain earth formations exhibit aproperty called “anisotropy”, wherein the velocity of acoustic wavespolarized in one direction may be somewhat different than the velocityof acoustic waves polarized in a different direction within the sameearth formation. See, for example, S. Crampin, A Review of the Effectsof Anisotropic Layering on the Propagation of Seismic Waves, Geophys. J.R. Astr. Soc., vol. 49, pp 9-27, 1977, incorporated herein by referenceas if reproduced in full below. Anisotropy may arise from intrinsicstructural properties, such as grain alignment, crystallization, alignedfractures, or from unequal stresses within the formation. Anisotropy isparticularly of interest in the measurement of the velocity ofshear/flexural waves propagating in the earth formations. Shear or Swaves are often called transverse waves because the particle motion isin a direction “transverse”, or perpendicular, to the direction that thewave is traveling.

Acoustic waves travel fastest when the direction of particle motionpolarization direction) is aligned with the material's stiffestdirection. If the formation is anisotropic, meaning that there is onedirection that is stiffer than another, then the component of particlemotion aligned in the stiff direction travels faster than the wavecomponent aligned in the other, more compliant direction in the sameplane. A shear wave induced into an anisotropic formation splits intotwo components, one polarized along the formation's stiff (or fast)direction, and the other polarized along the formation's compliant (orslow) direction Generally, the orientation of these two polarizations issubstantially orthogonal (components which are at a 90° angle relativeto each other). The fast wave is polarized along the direction parallelto the fracture strike and a slow wave in the direction perpendicular toit.

Acoustic well logging techniques have been devised for determining theamount of anisotropy from the shear wave velocities (slowness), and theamount of anisotropy is generally defined as the difference between thevelocities of the fast and the slow shear waves. One method ofdetermining fast and slow shear wave velocities and orientations uses anacoustic logging tool 100, as shown in FIG. 1, to detect components ofthe acoustic signals at several levels of dipole receivers. See, forexample U.S. Pat. No. 5,712,829 (hereinafter “the '829 patent”) issuedto Tang et al., incorporated herein by reference as if reproduced infull below.

In the '829 patent, two dipole sources X and Y, 102, are orientedorthogonal to each other. Signals detected by the dipole receivers A104, parallel to the X source, are referred to as XA signals when the Xsource is triggered. Similarly, signals detected by dipole receivers B106, parallel to the Y source 102, are referred to as YB signals whenthe Y source is triggered. Cross-component signals can also be detectedby the perpendicular receivers when each source is energized, and thesesignals are referred to as the XB and YA signals for the X and Y sourcesrespectively. Thus, a total of four sets of signals are created for eachdipole receiver pair for each set of firings of the sources X and Y.

Each of the four sets of signals can be represented as a time series,each of which consists of a series of numbers indexed with respect toincreasing time from the instant at which the respective source isenergized. The abscissa value in each series of numbers representsamplitude of the received signal. It must be understood, however, thatthe signal received by any particular receiver, regardless of whichtransmitter was fired, contains information about both the fast and theslow waves. Stated otherwise, the signal received by any particulardipole receiver is a combination of the signal induced by the fast waveand the signal induced by the slow wave. Determining the slowness of thefast and slow waves involves separating the fast and slow signals fromthe actual received signals. Various solutions to determine the fast andslow waveforms from the received signals incorporating both exist, forexample, in U.S. Pat. No. 4,817,061 issued to Alford et al.,incorporated herein by reference as if reproduced in fall below. Oncethe fast and slow waveforms are decomposed from the composite receivedwaveforms, prior art acoustic determinations are made as to the slownessof each of the waves. In particular, this slowness determinationtypically involves determining a coherence/semblance of the decomposedwaveforms.

While semblance may create visually pleasing results, determiningslowness in this matter is unsuitable for error estimation.Consequently, an improved method to determine fast and slow shear wavevelocity and orientation in an anisotropic formation is desired.

SUMMARY OF SOME OF THE PREFERRED EMBODIMENTS

The preferred embodiments of the present invention comprise a method andapparatus for determining the slowness and orientation of the fast andslow shear waves in an anisotropic earth formation. The apparatus formaking this determination preferably comprises two dipole transmitters,oriented substantially perpendicular to each other, mounted on a tooland designed for imparting acoustic energy into the surroundingformation. The tool further comprises a plurality of dipole receiverpairs, the receiver pairs spaced apart from each other and from thedipole transmitters. The dipole receivers in each dipole receiver pairare preferably oriented substantially perpendicular to each other. Thepreferred method of operation involves firing each dipole transmitter ateach depth level sequentially, and obtaining a plurality of receivedcomposite signals with the dipole receivers, as the tool is slowlyraised or lowered in the borehole. Each of the received signals is acomposite signal containing information about the fast and slow shearwaves. Each receiver pair on the same elevation creates four receivedsignals for each set of transmitter firings.

A plurality of transfer functions of the formation are assumed and aseries of source waveforms or wavelets are estimated using the receivedwaveforms and the assumed transfer functions. More particularly, thepreferred embodiments assume a transfer function for the formation atissue, and then estimate, using each set of received signals, a seriesof source signals that created the received signals based on the assumedtransfer function. An objective function is created which is indicativeof the similarity of the estimated source signals. Because the actualsource signals are preferably the same, a low value of the objectivefunction indicates that the assumed formation transfer function wasclose to the actual formation transfer function. The source estimationpreferably is repeated using multiple transfer functions (assumed strikeangles and slowness values). The values of the objective functioncalculated are preferably plotted in a starting time verses slownessverses strike angle graph, with the strike angle being the ordinate, theslowness being the abscissa, and the starting time being the Z axiscoordinate. Thus, for a series of assumed transfer functions, all at aparticular single strike angle, a vertical plane of information iscreated. The process is repeated for a series of assumed strike anglesranging from −90° to +90° (for a total of 180°), and at a plurality ofslowness values within each assumed transfer function. From mini in thegraph, the orientations of the fast and slow axis may be determined, thedifference in slowness between the fast and slow waves maybe determined,and the error of the slowness calculation determined.

The disclosed device comprises a combination of features and advantageswhich enable it to overcome the deficiencies of the prior art devices.The various characteristics described above, as well as other features,will be readily apparent to those skilled in the art upon reading thefollowing detailed description, and by referring to the accompanyingdrawings.

BRIEF DESCRIPTION OF THE DRAWINGS

For a more detailed description of the preferred embodiments of thepresent invention, reference will now be made to the accompanyingdrawings, wherein:

FIG. 1 shows a prior art acoustic logging tool;

FIG. 2 shows a wireline acoustic Jogging tool of the preferredembodiment;

FIG. 3 shows an exemplary set of decomposed received signals;

FIG. 4 shows an exemplary plot indicating how objective function valuesare placed in the plots of the preferred embodiment; and

FIG. 5 shows a black and white exemplary plot of an objective functionagainst slowness and strike angle.

NOTATION AND NOMENCLATURE

Certain terms are used throughout the following description and claimsto refer to particular system components. This document does not intendto distinguish between components that differ in name but not function.In the following discussion and in the claims, the terms “including” and“comprising” are used in an open-ended fashion, and thus should beinterpreted to mean “including, but not limited to . . . ”

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

FIG. 2 shows an acoustic logging device 10 constructed in accordancewith the preferred embodiments. In particular, FIG. 2 shows the tool 10disposed within a fluid filled borehole 12 at some distance below thesurface 14. The tool 10 is preferably suspended within the borehole bymeans of a multi-conductor armored cable 16. Thus, the tool 10 of thepreferred embodiment is a wireline device. However, it must beunderstood that the principles described herein may likewise bepracticed in a measuring-while-drilling (MWD) or logging-while-drilling(LWD) system.

The tool 10 preferably comprises a set of dipole transmitters: a firstdipole transmitter 20, and a second dipole transmitter 22. In theperspective view of FIG. 2, only one face of each of the dipoletransmitters 20, 22 may be seen. However, one of ordinary skill in theart understands that a complimentary face of each dipole transmitter 20and 22 is present on a back surface of the tool 10. The dipoletransmitters each may be a single dipole transmitter extending throughthe center of the tool 10, or may be individual transmitters fired insuch a way as to act in a dipole fashion. The transmitter 20 induces itsacoustic energy along an axis, which for convenience of discussion islabeled X in the FIG. 2. Transmitter 22 preferably induces energy alongits axis labeled Y in FIG. 2, where the X and Y axes (and thereforetransmitters 20, 22) are preferably orthogonal. The orthogonalrelationship of the transmitters 20, 22 need not necessarily be thecase, but a deviation from an orthogonal relationship complicates thedecomposition of the waveforms.

Tool 10 also comprises a plurality of receiver pairs at elevationsspaced apart from the transmitters 20, 22. In particular, the preferredembodiment comprises four pairs of dipole receivers. However, any numberof receiver pairs may be used without departing from the spirit andscope of the invention. In FIG. 2, the receivers are labeled 24A-D and26A-D. Preferably, each set of dipole receivers at a particularelevation has one receiver whose axis is coplanar with the axis oftransmitter 20 (in the X direction) and one receiver whose axis iscoplanar with the axis of transmitter 22 (in the Y direction). Forexample, one set of dipole receivers could be receivers 24A and 26A.Thus, the dipole receivers whose axes are coplanar with the axis oftransmitter 20 are the transmitters 24A-D. Likewise the dipole receiverswhose axes are coplanar with the axis of transmitter 22 are receivers26A-D. While it is preferred that the axes of the receivers be coplanarwith the axes of one of the transmitters, this is not required. However,azimuthly rotating any of the receiver pairs complicates thetrigonometric relationships and, therefore, the data processing.

In broad terms, the processing method of the preferred embodimentcomprises calculating or estimating source signals or source waveletsthat created each set of received signals by assuming a transferfunction of the formation. Estimating source wavelets can be describedmathematically as follows:

S _(EST) _(i) (t)=[TF] ⁻¹ R _(i)(t)   (1)

where S_(EST) _(i) is the estimated source signal calculated for the ithset of receivers, [TF] is the assumed transfer function of the formationin the source to receiver propagation, and R_(i) is the decomposedwaveforms (described below) for the ith receiver set. Thus, for each setof received signals R_(i), an estimate of the source signal S_(EST) _(i)is created. The estimated source signals are compared in some way tocreate an objective function. Minimas of a graph of the objectivefunction are indicative of the angle of the anisotropy, and the slownessof the acoustic waves through the formation. Further, depending on thetype objective function used, one or both of the value of the objectionfunction at the minimas, and the curvature of the of the objectivefunction plot near the minimas, are indicative of the error of theslowness determination.

Thus, a primary component of the source signal estimation is the assumedtransfer function [TF]. The transfer function may be relatively simple,taking into account only the finite speed at which the acoustic signalspropagate and the strike angle, or may be very complex, to includeestimations of attenuation of the transmitted signal in the formation,paths of travel of the acoustic signals, the many different propagationmodes within the formation (e.g. compressional waves, sheer waves,Stonely waves), and if desired even the effects of the acoustic wavescrossing boundaries between different layers of earth formations. Forreasons of simplicity of the calculation, the preferred estimatedtransfer functions take into account only the propagation speed(slowness) of the acoustic energy in the formation and the strike angleof the anisotropy.

As discussed in the Background section, anisotropic earth formationstend to break an induced shear wave into two components: one of thosecomponents traveling along the faster polarization direction, and thesecond component traveling along the slower polarization direction,where those two directions are substantially orthogonal. Therelationship of the fast and slow polarizations within the formation,however, rarely lines up with the orthogonal relationship of the dipoletransmitters 20, 22. For convenience of the following discussion andmathematical formulas, a strike angle θ is defined to be the anglebetween the X direction orientation (the axis of dipole transmitter 20)and the faster of the two shear wave polarizations (see FIG. 2).Further, it must be understood that the shear wave of interest does notpropagate in the X or Y direction, but instead propagates in the Zdirection along the borehole wall.

Operation of the tool 10 involves alternative firings of thetransmitters 20, 22. Each of the receivers 24A-D and 26A-D createreceived waveforms designated R, starting at the firing of a particulartransmitter. Each of the received waveforms or signals has the followingnotation: R_([receiver][source]). Thus, for the firing of transmitter 20in the X direction, and receipt by one of the receivers having an axiscoplanar to the axis of transmitter 20 (receivers 24A-D), the timeseries received signal is designated as R_(XX). Likewise, thecross-component signal, the signal received by the dipole receiver whoseaxis is substantially perpendicular to the axis of the firingtransmitter, is designated R_(YX) in this situation. In similar fashion,firing of the transmitter whose axis is oriented in the Y direction,transmitter 22, results in a plurality of received signals designated asR_(YY) for the axially parallel receivers, and R_(XY) for thecross-components. Thus, each transmitter firing creates two receivedsignals, one for each receiver of the dipole receiver pair. It followsthat for a set of dipole transmitter firings, four signals are receivedat each receiver pair indicative of the acoustic signals propagatedthrough the formation.

Each of the received signals in the case described above containscomponents of both the fast and slow shear waves—composite signals. Thatis, for example, an R_(XX) receiver signal contains informationregarding both the fast and slow polarized signals. These compositesignals may be decomposed into their fast and slow components usingequations as follows:

FP(t)=cos²(θ)R _(XX)(t)+sin(θ)cos(θ)[R _(XY)(t)+R _(YX)(t)]+sin²(θ)R_(YY)(t)   (2)

SP(t)=sin²(θ)R _(XX)(t)−cos(θ)sin(θ)[R _(XY)(t)+R _(YX)(t)]+cos²(θ)R_(YY)(t)   (3)

sin(2θ)[R _(XX)(t)−R _(YY)(t)]−cos(2θ)[R _(XY)(t)+R _(YX)(t)]=0   (4)

where FP(t) is the fast polarization time series, SP(t) is the slowpolarization time series, and θ is the strike angle as defied above. Theprior art technique for decomposing the multiple received compositesignals involved determining the strike angle θ by solving equation (4)above, and using that strike angle in equations (2) and (3) to decomposethe composite signals into the fast and slow time series. The preferredembodiments of this invention take a different tact.

A close inspection of equations (2) and (3) above for the fast and slowpolarization time series respectively shows two very symmetricequations. Taking into account the trigonometric relationships:

sinθ=cos(90°−θ)   (5)

cosθ=sin(90°−θ)   (6)

it may be recognized that either the fast polarization equation (2) orthe slow polarization equation (3) may be used to obtain either the fastor slow polarization signals by appropriately adjusting the angle θ usedin the calculation. Stated otherwise, either the fast or slowpolarization equations (2) or (3) may be used to decompose a receivedsignal having both fast and slow components into individual componentsif the strike angle θ is appropriately adjusted.

Rather than using a single strike angle in both equations (2) and (3)above, in the preferred embodiments each assumed transfer functioncomprises a strike angle. A plurality of transfer functions are assumedover the course of the slowness determination, and thus a plurality ofstrike angles are used, preferably spanning possible strike angles from−90° to +90° (180°). For each assumed transfer function (and thus strikeangle), the four received signals generated by a set of receivers ateach elevation are decomposed using the following equation:

DS(t)cos²(θ)R _(XX)(t)+sin(θ)cos(θ)[R _(XY)(t)+R _(YX)(t)]+sin²(θ)R_(YY)(t)   (7)

where DS(t) is simply the decomposed signal for the particular strikeangle used. This process is preferably repeated for each set of receivedsignals at each level for each assumed transfer function. Equation (7)is equation (2) above; however, equation (3) may be equivalently used ifthe assumed strike angle is appropriately adjusted.

FIG. 3 shows an exemplary set of four decomposed signals that in thepreferred embodiment are created using equation (7) above for aparticular transfer function (strike angle). In the exemplary set ofdecomposed signals, R1 could be the decomposed signal created using thestrike angle from the assumed transfer function and the compositesignals received by the set of receivers 24A, 26A. Likewise, decomposedsignal R2 could be the decomposed signal created again using the strikeangle from the assumed transfer function and the composite signalscreated by the set of receivers 24B, 26B. Notice how the amplitude ofthe decomposed signal of the set of receivers closest to thetransmitters, decomposed signal R1, is greater than the decomposedsignals of the more distant receivers, for example R4. Note also how thewaveforms shift out in time from the closest to the more distantreceivers, which is indicative of the finite speed of the acoustic waveswithin the formation.

For a particular starting time within the decomposed signals, forexample starting time T₁ in FIG. 3, and for a first assumed transferfunction having an assumed strike angle and slowness, portions of eachdecomposed signal are identified as being related based on the transferfunction. Rectangular time slice 50 of FIG. 3 is representative of aslowness in an assumed transfer function (with the assumed strike angleused to create the decomposed signals exemplified in FIG. 3). Inparticular, the slope of the rectangular time slice is indicative of theslowness of the assumed transfer function. Stated another way, theportions of the decomposed signals within the rectangular time slice 50should correspond based on the assumed slowness of the formation of thetransfer function. The time width of the samples taken from each of thereceived signals is preferably at least as long as each of the sourcesignals in a firing set. In this way, an entire source waveform orsource wavelet may be estimated. However, the time width of the samplestaken from the decomposed signals need not necessarily be this width, asshorter and longer times would be operational.

Thus, the portions of the decomposed signals in the rectangular timeslice 50 are each used to create an estimated source signal. Theseestimated source signals are compared to create an objective functionthat is indicative of their similarity. The process of assuming atransfer function, estimating source wavelets based on decomposedsignals and creating an objective function is repeated a plurality oftimes. The rectangular time slices 50 through 54 are exemplary ofmultiple assumed transfer functions used in association with startingtime T₁ (and the a strike angle used to create the decomposed signals).Estimating source wavelets in this fashion (including multiple assumedtransfer functions) is preferably also repeated at multiple startingtimes within the decomposed signals, represented in FIG. 3 as T₁, T₂ . .. T_(N).

The value of the objective function created for each assumed transferfunction and starting time is preferably plotted in a graph as afunction of the starting time and the slowness of assumed transferfunction. As shown in FIG. 4, the starting time of the source signalestimations, T₁, T₂ . . . T_(n), are preferably the Z axis coordinate(assumed strike angle is the ordinate or X axis (not shown in FIG. 4),as is discussed more below) and the slowness is preferably the abscissaor Y axis. Thus, for example, the value of the objective functioncalculated using portions of decomposed signals R₁-R₄ within rectangulartime slice 50 is plotted at point 60 in FIG. 4. Likewise, the value ofthe objective function associated with the assumed slowness implied byrectangular time slice 52 is plotted at point 62, and the value of theobjective function associated with the rectangular time slice 54 isshown at point 64. Thus, for each of a plurality of starting times, andfor each starting time a plurality of slowness values associated withassumed transfer functions, a graph of the objective function iscreated. In the preferred embodiments, the value of the objectivefunction is indicated by a color, with cooler colors (blues, purples)showing more similarity, and hotter colors (reds, oranges) showing lesssimilarity of the estimated source signals or source wavelets. The colorschemes however are only exemplary and other schemes may be used withoutdeparting from the scope and spirit of the invention.

Calculating the objective function of the a first embodiment preferablycomprises comparing estimated source signals to determine a variancebetween them. More particularly, this slowness determination preferablycomprises calculating an average of the estimated source signals withineach time slice, and then calculating a variance against the averagesource signal. In more mathematical terms, for each assumed transferfunction, a series of estimated source waveforms or signals S_(EST) _(i)are calculated using equation (1) above. From these estimated sourcesignals, an average estimated source signal is preferably calculated asfollows: $\begin{matrix}{{S_{{EST}_{AVG}}(t)} = {\frac{1}{N}{\sum\limits_{i = 1}^{N}{S_{{EST}_{i}}(t)}}}} & (8)\end{matrix}$

where S_(EST) _(AVG) is the average estimated source signal, N is thenumber of decomposed received signals, S_(EST) _(i) is the sourcewavelet estimated for each decomposed received signal within the timeslice, and t is time within the various time series.

The average estimated source signal is used to calculate a valuerepresenting the variance of the estimated source signals from theaverage estimated source signal. The variance is preferably calculatedas follows: $\begin{matrix}{\delta^{2} = {\sum\limits_{i = 1}^{N}( {{S_{{EST}_{i}}(t)} - {S_{{EST}_{AVG}}(t)}} )^{2}}} & (9)\end{matrix}$

where δ² is the variance. In one embodiment, the variance value is theobjective function plotted in the slowness versus starting time versusstrike angle graph Large values of the variance indicate that theassumed transfer function (assumed strike angle and/or assumed slowness)did not significantly match the actual formation properties. Likewise,small values of the variance indicate that the assumed transfer functionclosely matched the actual formation properties. Thus, the minimas ofthe objective function in the plot described above indicate the slownessof the fast and slow polarized waves as well as the actual strike angle(this determination further exemplified in the discussion with respectto FIG. 5 below). The value of the variance objective function at theminimas is indicative of the error of the determination of the acousticvelocity and strike angle. Relatedly, the curvature of the varianceobjective function plot at the minima is indicative of the error of thecalculation.

A second embodiment for calculating an objective function is based ondetermining a difference between each estimated source signal. Inparticular, and referring again to FIG. 3, consider the portions of thedecomposed signals within rectangular time slice 50 associating withstarting time T₁. As discussed above, using the assumed transferfunction, an estimated source signal is created using the portions ofthe decomposed signal within the time slice 50. Differences ordifferentials are calculated between each estimated source signal, forexample between the source signal estimated from a portion of the R1signal and the source signal estimated from the portion of the R2signal. This difference is preferably calculated between each succeedingreceiver, and the objective function in this embodiment is the sum ofthe square of each difference calculation. Much like plotting thevariance objective function, this differential objective function ispreferably plotted as a function of slowness, starting time and strikeangle. However, the graph obtained using the differential slownesscalculation has slower transitions from maximas to minimas whichtherefore makes determining the minimas (indicative of the actualslowness of the fast and slow polarizations) easier than in cases wherethe graph has relatively steep slopes between minima and maxima Moremathematically, the objective function of this second embodiment iscalculated as follows: $\begin{matrix}{\zeta = {\sum\limits_{i = 1}^{N - 1}( {S_{{EST}_{i + 1}} - S_{{EST}_{i}}} )^{2}}} & (10)\end{matrix}$

where ζ is the objective function, and N is the number of receivers.Much like using the variance as the objective function, thisdifferential objective function is preferably plotted in a slownessversus starting time versus strike angle graph, with cooler colorsrepresenting less difference between received signals, and hotter colorsrepresenting greater differences. Known techniques may be used todetermine minima of these graphs, and the locations of the minima areindicative of formation slowness and the strike angle.

Neither of the two embodiments of calculating objective functionsdescribed above, variance and differential, are more preferred, as eachhave their own advantages. Plots of the variance objective value havesteep slopes between maxima and minima, and thus the minima are betterdefined and the results more accurate. However, the differentialobjective value system has slower transitions from maxima to minima,making the determination of the minima by computer program easier. Thus,either may be used in any particular circumstance, and it is possiblethat both may be used in a single system.

FIG. 5 shows a black and white version of an exemplary slice (to createa two dimension graph) of a three dimensional graph of the objectivefunction of the preferred embodiment. With reference to FIG. 3,preferably slowness is the abscissa, starting time is the Z coordinate,and strike angle is the ordinate (extending out of the page). The plotof FIG. 5 is a vertical slice of the three dimensional plot at aparticular starting time, e.g. T1, such what is produced is a twodimensional plot as a function of slowness and strike angle. As can beseen from FIG. 5, the slower of the two polarized shear waves has aslowness of approximately 140 micro-seconds per foot (μs/ft), and ispolarized at approximately −45°. Likewise, the faster of the twopolarized waves has a slowness of approximately 125 μs/ft, and ispolarized at approximately +45°. As discussed above, the two regions oflower objective function values are preferably plotted in color, withlower objective function values taking on cooler colors. FIG. 5 however,being black and white, shows these only as darker shades of gray. Byanalyzing the three dimensional plot, using known techniques, to findminimas of the objective function, characteristics of the formation maybe determined. These characteristics may comprise the fast and slowshear wave velocities, strike angle of the anisotropy (as well as therelative angle between the two waves), and an indication of the error inthe calculation (the value of the objective function at the minimas).Another error indication is the calculated difference in angle betweenthe fast and slow wave. Theoretically, the angle should be 90 degrees. Adeparture from the 90 degree theoretical value may be used as anestimate of the error of the strike angle calculation.

Numerous variations and modifications will become apparent to thoseskilled in the art once the above disclosure is fully appreciated. Forexample, the disclosed method for determining shear wave velocity andorientation may be implemented using any number of receiver levels anddifferent receiver types for the acoustic logging tool. Indeed, even asingle set of dipole receivers may be used relying on rotation of thetool to obtain additional composite signals for decomposition. Further,the source may be located at any arbitrary angle relative to thereceivers. Moreover, processing of the data after collection atreceivers can be performed downhole in real time with only the resultsbeing transferred uphole to a computer system for storage. Throughoutthis discussion, the various earth formation characteristics werediscussed with reference to finding minimas of the objective function.However, one of ordinary skill in the art could easily invert the valuesused, thus making a determination a search for maximum values in theplot, and this would not deviate from the scope and spirit of theinvention. While assuming the transfer functions in the embodimentsdescribed involved also assuming a strike angle, it is possible that thetransfer function need not include a strike angle estimation, andinstead the composite signals could be decomposed for the range ofpossible strike angles independent of an assumed transfer function.Relatedly, it is possible to solve for the strike angle using equation(4) above and decompose the composite waveforms using that strike angle;and thereafter, estimate and apply transfer functions to the decomposedsignals, thus also removing the strike angle from the transfer function.It is intended that the following claims be interpreted to embrace allsuch variations and modifications.

What is claimed is:
 1. A method of determining characteristics of ananisotropic earth formation, the method comprising: transmittingacoustic energy into the earth formation, and wherein the earthformation breaks the acoustic energy into a fast polarization shear waveand a slow polarization shear wave; receiving composite waveformscomprising components of both the, fast and slow polarization shearwaves; decomposing the composite waveforms into decomposed waveforms;estimating source waveforms from the decomposed waveforms to createestimated source waveforms; and comparing the estimated source waveformsto determine characteristics of the anisotropic earth formation.
 2. Themethod of determining characteristics of an anisotropic earth formationas defined in claim 1 wherein transmitting acoustic energy into theearth formation further comprises: firing a first dipole transmitter ina first axial direction; then firing a second dipole transmitter in anaxial direction substantially azimuthaly perpendicular to the firstaxial direction.
 3. The method of determining characteristics of ananisotropic earth formation as defined in claim 2 wherein receivingcomposite waveforms comprising components of both the fast and slowpolarization shear waves further comprises: receiving a first set ofcomposite waveforms with a first dipole receiver pair associated withthe firing of the first dipole transmitter; receiving a second set ofcomposite waveforms with a second dipole receiver pair associated withthe firing of the first dipole transmitter; receiving a third set ofcomposite waveforms with the first dipole receiver pair associated withthe firing of the second dipole transmitter; and receiving a fourth setof composite waveforms with the second dipole receiver pair associatedwith the firing of the second dipole transmitter.
 4. The method ofdetermining characteristics of an anisotropic earth formation as definedin claim 3 wherein decomposing the composite waveforms into decomposedwaveforms further comprises: estimating a transfer function of theanisotropic earth formation comprising at least a strike angle for theanisotropy and an acoustic velocity; decomposing the first and third setof composite waveforms using the strike angle to create a firstdecomposed waveform; decomposing the second and fourth compositewaveforms to create a second decomposed waveform; and applying theinverse of the estimated transfer function to the decomposed waveformsto create the estimated source waveforms.
 5. The method of determiningcharacteristics of an anisotropic earth formation as defined in claim 1wherein comparing the estimated source waveforms to determine thecharacteristic of the anisotropic earth formation further comprises:calculating an objective function based on the estimated sourcewaveforms; and determining the characteristic of the anisotropic earthformation based on a plot containing the objective function.
 6. Themethod of determining characteristics of an anisotropic earth formationas defined in claim 5 wherein calculating an objective function based onthe estimated source waveforms further comprises: averaging theestimated source waveforms to determine an average estimated sourcewaveform; and determining a variance value of the estimated sourcewaveforms using the average estimated source waveform, the variancevalue being the objective function.
 7. The method of determiningcharacteristics of an anisotropic earth formation as defined in claim 6wherein averaging the estimated source waveforms to determine an averageestimated source waveform further comprises determining the averageestimated source waveform using substantially the following equation:${S_{{EST}_{AVG}}(t)} = {\frac{1}{N}{\sum\limits_{i = 1}^{N}{S_{{EST}_{i}}(t)}}}$

where S_(EST) _(AVG) is the average estimated source waveform, N is thenumber of decomposed waveforms used to create the average estimatedsource signal, S_(EST) _(i) is the estimated source waveform for eachdecomposed waveform, and t is time.
 8. The method of determiningcharacteristics of an anisotropic earth formation as defined in claim 6wherein determining a variance value of the estimated source waveformsusing the average estimated source waveform further comprises:$\delta^{2} = {\sum\limits_{i = 1}^{N}( {{S_{{EST}_{i}}(t)} - {S_{{EST}_{AVG}}(t)}} )^{2}}$

where δ² is the variance, S_(EST) _(AVG) is the average estimated sourcewaveform, N is the number of decomposed waveforms used to create theaverage estimated source signal, S_(EST) _(i) is the estimated sourcewaveform for each decomposed waveform, and t is time.
 9. The method ofdetermining characteristics of an anisotropic earth formation as definedin claim 6 further comprising: plotting multiple variance valuescalculated for multiple sets of estimated source waveforms; anddetermining inflection points of the variance values within the plot asindicative of acoustic velocity within the earth formation.
 10. Themethod of determining characteristics of an anisotropic earth formationas defined in claim 9 wherein comparing the estimated source waveformsto determine the acoustic velocity further comprises finding locationswhere the inflection points are minimas.
 11. The method of determiningcharacteristics of an anisotropic earth formation as defined in claim 10further comprising estimating an error in the determination of thecharacteristic of the anisotropic earth formation based on a value ofthe objective function at the minimas.
 12. The method of determiningcharacteristics of an anisotropic earth formation as defined in claim 10further comprising estimating an error in the determination of thecharacteristic of the anisotropic earth formation based on a curvatureof the plot of the value of the objective function at the minimas. 13.The method of determining characteristics of an anisotropic earthformation as defined in claim 1 wherein comparing the estimated sourcewaveforms to determine the acoustic velocity further comprises:calculating a differences between each estimated source waveforms toobtain an objective function using substantially the following equation:$\zeta = {\sum\limits_{i = 1}^{N - 1}( {S_{{EST}_{i + 1}} - S_{{EST}_{i}}} )^{2}}$

where ζ is the objective function, and N is the number of decomposedwaveforms, and S_(EST) _(i) is the estimated source waveform for eachdecomposed waveform.
 14. The method of determining characteristics of ananisotropic earth formation as defined in claim 13 wherein comparing theestimated source waveforms to determine the acoustic velocity furthercomprises: plotting multiple values of the objective function calculatedfor multiple sets of estimated source waveforms; and determininginflection points of the values of the objective function within theplot as indicative of acoustic velocity within the earth formation. 15.The method of determining characteristics of an anisotropic earthformation as defined in claim 14 wherein comparing the estimated sourcewaveforms to determine the acoustic velocity further comprises findinglocations where the inflection points are minimas.
 16. The method ofdetermining characteristics of an anisotropic earth formation as definedin claim 15 wherein an error in the determination of the acousticvelocity is proportional to the a curvature of the values of theobjective function at the minimas.
 17. The method of determiningcharacteristics of an anisotropic earth formation as defined in claim 1wherein comparing the estimated source waveforms to determinecharacteristics of the anisotropic earth formation further comprisescomparing the estimated source waveforms to determine at least one ofthe fast and slow polarization shear wave acoustic velocities.
 18. Themethod of determining characteristics of an anisotropic earth formationas defined in claim 1 wherein comparing the estimated source waveformsto determine characteristics of the anisotropic earth formation furthercomprises comparing the estimated source waveforms to determine a strikeangle of the anisotropy.
 19. The method of determining characteristicsof an anisotropic earth formation as defined in claim 18 furthercomprising determining an error estimate of the strike angle bycomparing an angle between the fast and slow polarization shear waves.20. In an anisotropic earth formation where an induced shear wave breaksup into a fast polarization component and a slow polarization component,a method of determining characteristics of the earth formationcomprising: a) generating acoustic signals with dipole transmitter pairby firing a first dipole transmitter, then firing a second dipoletransmitter; b) receiving at a first dipole receiver pair acousticenergy composite signals containing information about both the fast andslow polarization components; c) receiving at a second dipole receiverpair acoustic energy composite signals containing information about boththe fast and slow polarization components; d) decomposing the signals ofthe first dipole receiver pair into a first decomposed signal for astrike angle; e) decomposing the signals of the second dipole receiverpair into a second decomposed signal for the strike angle; f) estimatinga an assumed slowness of the earth formation; g) estimating a firstsource wavelet based on the first decomposed signal; h) estimating asecond source wavelet based on the second decomposed signal; i)comparing the first and second source wavelets to obtain an objectivefunction; j) plotting the objecting function as a function of slownessof the assumed transfer function, a start time within the decomposedsignals, and strike angle; k) repeating steps f) through j) for aplurality of assumed transfer functions; l) repeating steps f) throughk) for a plurality of start times within the decomposed signal; and m)repeating steps d) through l) for a plurality of strike angles.
 21. Themethod of determining characteristics of an earth formation as definedin claim 20 wherein decomposing the signals of the first dipole receiverpair into a first decomposed signal further comprises calculating thefirst decomposed signal using substantially the following equation:DS(t)=cos² (θ) R _(XX)(t)+sin(θ)cos(θ) [R _(XY) (t)+R _(YX)(t)]+sin²(θ)R_(YY)(t) where DS(t) is the decomposed signal, θis the strike angle,R_(XX) is a signal received by a first receiver of the first receiverpair with an axis oriented in an X direction when a transmitter in the Xdirection is fired, R_(YX) is a signal received by the first receiver ofthe first receiver pair when a transmitter in a transmitter in the Ydirection is fired, R_(YX) is a signal received by a second receiver ofthe first receiver pair with an axis oriented in the Y direction whenthe transmitter oriented in the X direction is fired, and R_(YY) is asignal received by the second receiver oriented in the Y direction whenthe transmitter oriented in the Y direction is fired.
 22. The method ofdetermining characteristics of an earth formation as defined in claim 20wherein decomposing the signals of the second dipole receiver pair intoa second decomposed signal further comprises calculating the firstdecomposed signal using substantially the following equation:DS(t)=cos²(θ)R _(XX)(t)+sin(θ)cos(θ) [R _(XY) (t)+R _(YX)(t)]+sin²(θ)R_(YY)(t) where DS(t) is the decomposed signal, θis the strike angle,R_(XX) is a signal received by a first receiver of the second receiverpair with an axis oriented in an X direction when a transmitter in the Xdirection is fired, R_(XY) is a signal received by the first receiver ofthe second receiver pair when a transmitter in a transmitter in the Ydirection is fired, R_(YX) is a signal received by a second receiver ofthe second receiver pair with an axis oriented in the Y direction whenthe transmitter oriented in the X direction is fired, and R_(YY) is asignal received by the second receiver oriented in the Y direction whenthe transmitter oriented in the Y direction is fired.
 23. The method ofdetermining a characteristic of an earth formation as defined in claim20 wherein comparing the first and second source wavelets to obtain anobjective function further comprises: calculating an average estimatedsource wavelet; and calculating a variance of the estimated sourcewavelets from the average estimated source wavelet.
 24. The method ofdetermining a characteristic of an earth formation as defined in claim23 wherein calculating the average estimated source wavelet furthercomprises calculating the average estimated source wavelet usingsubstantially the following equation:${S_{{EST}_{AVG}}(t)} = {\frac{1}{N}{\sum\limits_{i = 1}^{N}{S_{{EST}_{i}}(t)}}}$

where S_(EST) _(AVG) is the average estimated source signal, N is thenumber estimated source wavelets, S_(EST) _(i) is the estimated sourcewavelet, and t is time.
 25. The method of determining a characteristicof an earth formation as defined in claim 24 wherein calculating avariance of the estimated source wavelets from the average estimatedsource wavelet further comprises calculating the variance usingsubstantially the following equation:$\delta^{2} = {\sum\limits_{i = 1}^{N}( {{S_{{EST}_{i}}(t)} - {S_{{EST}_{AVG}}(t)}} )^{2}}$

where δ² is the variance.
 26. The method of determining a characteristicof an earth formation as defined in claim 20 wherein comparing the firstand second source wavelets to obtain an objective function furthercomprises determining a difference between the estimated source waveletsas the objective function.
 27. The method of determining acharacteristic of an earth formation as defined in claim 26 whereindetermining a difference between the estimated source wavelets furthercomprises calculating an objective function using substantially thefollowing equation:$\zeta = {\sum\limits_{i = 1}^{N - 1}( {S_{{EST}_{i + 1}} - S_{{EST}_{i}}} )^{2}}$

where ζ is the objective function, S_(EST) _(i) is the estimated sourcewavelet, and N is the number of estimated source wavelets.